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Comparing Clusterings by the Variation of Information

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Learning Theory and Kernel Machines

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2777))


This paper proposes an information theoretic criterion for comparing two partitions, or clusterings, of the same data set. The criterion, called variation of information (VI), measures the amount of information lost and gained in changing from clustering \({\cal C}\) to clustering \({\cal C}'\). The criterion makes no assumptions about how the clusterings were generated and applies to both soft and hard clusterings. The basic properties of VI are presented and discussed from the point of view of comparing clusterings. In particular, the VI is positive, symmetric and obeys the triangle inequality. Thus, surprisingly enough, it is a true metric on the space of clusterings.

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© 2003 Springer-Verlag Berlin Heidelberg

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Meilă, M. (2003). Comparing Clusterings by the Variation of Information. In: Schölkopf, B., Warmuth, M.K. (eds) Learning Theory and Kernel Machines. Lecture Notes in Computer Science(), vol 2777. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40720-1

  • Online ISBN: 978-3-540-45167-9

  • eBook Packages: Springer Book Archive

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